Practice Problems for the College Algebra
Placement Exam
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Calculators are allowed.
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No charge to take the exam.
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THEA score must be between 230 and 249.
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Elementary Algebra ACCUPLACER score must be between 63 and 67
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The Exam is given everyday at 3:30 PM in Building J, Pecan - Room J-3.1102.
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Different Exam time might be available. Call
872-8327 to schedule another time.
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Free Tutoring is available at all success centers.
Call 872-6425 for more info.
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On Wednesday, the exam is also given at the Mid-Valley Center for Learning Excellence (Ph. 872-6600) at 10:00 a.m.
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Solve:
1. Parking Costs. A hospital parking lot charges $1.50 for the first hour or part thereof, and $1.00 for each additional hour or part thereof. A weekly pass costs $27.00 and allows unlimited parking for 7 days. Suppose that each visit Ed makes to the hospital lasts 1.5 hr. What is the minimum number of times that Ed would have to visit per week to make it worthwhile for him to buy the pass?
2. Van Rental. Value Rent-A-Car rents vans at a daily rate of $84.95 plus 60 cents per mile. Molly rents a van to deliver electrical parts to her customers. She is allotted a daily budget of $320. How many miles can she drive for $320?
3. Trigonometry. The second angle of a triangular field is three times as large as the first angle. The third angle is 40 degrees greater than the first angle. How large are the angles?
4. Triangular Parking Lot. The second angle of a triangular parking lot is four times as large as the first angle. The angle is 45 degrees less than the sum of the other two angles. How large are the angles?
5. Barn
Silo. A barn silo, excluding the
top, is a circular cylinder. The silo is
6 m in diameter and the height is 13 m.
Find the volume. Use 
for p.
6. Woodwork. A log of wood has a diameter of 12 cm and a height of 42 cm. Find the volume. Use 3.14 for p.
7. Tennis Ball. The diameter of a tennis ball is 6.5 cm. Find the volume. Use 3.14 for p.
8. Spherical Gas Tank. The diameter of a spherical gas tank is 6 m. Find the volume. Use 3.14 for p.
9. Volume of The Earth. The diameter of the earth is about 3980 mi. Find the volume of the earth. Use 3.14 for p. Round to the nearest ten thousand cubic miles.
10. Inscribed Spheres. The volume of a ball is 36p cm3. Find the dimensions of a rectangular box that is just large enough to hold the ball.
11. Dimensions of a Quarter. The circumference of a quarter is 7.85 cm. What is the diameter? The radius? The area?
12. Dimensions of a Dime. The circumference of a dime is 2.23 in. What is the diameter? The radius? The area?
13. Gypsy-Moth Tape. To protect an elm tree in your backyard, you need to attach gypsy moth caterpillar tape around the trunk. The tree has a 1.1-ft diameter. What length of tape is needed?
14. Silo. A silo has a 10 m diameter. What is its circumference?
15. Cans. The top of a soda can has a 6 cm diameter. What is its radius? Its circumference? Its area?
16. Pennies. A penny has a 1 cm radius. What is its diameter? Its circumference? Its area?
17. Radio Station. A radio station is allowed by the FCC to broadcast over an area with a radius of 220 mi. How much area is this?
18. Pizza Areas. Which is larger and by how much: a 12 in circular pizza or a 12 in square pizza?
19. Movies. Of all moviegoers, 67% are in the 12-29 age group. A theater held 800 people for a showing of Star Trek-18. How many were in the 12-29 age group? Not in this group?
20. Water.
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Rationalize the denominator:
1. 
2. 
3. 
4. 
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Factor each expression
completely. Indicate which ones are prime.
1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 
19. 
20. 
21. 
22. 
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24. 
25. 
26. 
27. 
28. 
29. 
30. 
31. 
32. 
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Simplify each fraction. Assume that no denominators are zero.
1. 
2. 
3. 
4. 
5. 
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Perform the operations and simplify whenever possible. Assume that no denominators are zero.
1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
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Simplify each complex fraction. Assume that no denominators are zero.
1.
2.
3.
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Simplify each expression. Assume that all variables represent positive numbers, so that no absolute value symbols are needed.
1.
2.
3.
4.
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Simplify each expression. Write all answers without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19. 
20.
Let x = -2, y = 0, and z = 3, evaluate each expression.
1. 
2. 
3. 
4. 
5. 
6. 
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Simplify each expression. Use absolute value symbols when necessary.
1. 
2. 
3. 
4. 
5. 
Simplify each expression. Write all answers without using negative exponents. Assume that all variables represent positive numbers.
1.
2.
3.
4.
5.
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Solve:
1.
65.12 is 74% of
what?
2.
63.7 is 65% of
what?
3.
What is 32% of
70?
4.
80% of 920 is
what?
5.
What is 6% of
2000?
6.
63.1% of 80 is
what?
7.
$24 is what
percent $96?
8.
102 is what
percent of 100?
9.
103 is what
percent of 100?
10. What percent of $480 is $120?
11. What percent of $80 is $60?
12. What percent of 33 is 11?
13. $75 is 20% of what?
Add:
1.
(3x5+5x3-5x2-3)+(x5+x4-3x3-3x2+2x-4)
2. 
Subtract:
1.
(2x4+x3-8x2-6x-3)-(6x4-8x2+2x)
2.
(x3-0.4x2-12)-(x5+0.3x3+0.4x2+9
Multiply:
1.
–3x2(4x2-3x-5)
2. 
3.
(3x+10)(3x-10)
4.
(3b+5)(b-3)
5.
(2x+1)(3x2-5x-3)
6.
(5t+2)2
Multiply and Simplify:
1.
6-2 *
6-3
2.
x6 * x2
* x
3.
(4a)3
* (4a)8
Divide and Simplify:
1. 
2. 
3. 
Simplify:
1.
(x3)2
2.
(-3y2)3
3.
(2a3b)4
4.
5.
(3x2)3(-2x5)3
6.
3(x2)3(-2x5)3
7.
2x2(-3x2)4
Solve:
1. Convert to scientific notation: 3,900,000,000
2. Convert to decimal notation: (5 X 10-8)
Multiply or divide and write scientific notation for the
answer:
1. 
2. (2.4 X 105)(5.4 X 1016)
Solve:
1. A CD-ROM can contain about 600 million pieces of information (bytes). How many sound files, each containing 40,000 bytes, can a CD_ROM hold? Express the answer in scientific notation.
2. Evaluate the polynomial x5+5x-1 for x = -2
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Multiply:
1. (x2+1)2
2. (8x-x2)2
3. (2-3x4)2
4. 
5. (0.3y+2.4)2
6. (3-2x3)2
7. (x-4x3)2
8. 4x(x2+6x-3)
9. 8x(-x5+6x2+9)
10. (2x2-½)(2x2-½)
11. (-x2+1)2
12. (-1+3p)(1+3p)
13. –6x2(x3+8x-9)
14. (6x4+4)2
15. (8a+5)2
16. (3x+2)(4x2+5)
17. (2x2-7)(3x2+9)
18. (y+5)(y2-5y+25)
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Multiply:
1. (3x5+2)(2x2+6)
2. (1-2x)(1+3x2)
3. (8x3+1)(x3+8)
4. (4x2+3)(x-3)
5. (7x-2)(2x-7)
6. (4y4+y2)(y2+y)
7. (x+4)(x-4)
8. (x4+3x)(x4-3x)
9. 
10. (12-3x2)(12+3x2)
11. (2y8+3)(2y8-3)
12. 
13. 
14. (a-½)2
15. 
16.
(3+x)2
17.
(x3-1)2
18.
(x3+x2)(x3+x2-x)
19.
(x3-x2)(x3-x2+x)
20.
(x-x3+x5)(x2-1+x4)
21.
(x-x3+x5)(3x2+3x6+3x4)
22.
(x3+x2+x+1)(x-1)
23.
(x+2)(x3-x2+x-2)
24. 
25. 
26. (-4m5)(-1)
Divide:
1. 
2. 
3. 
4. 
5. 
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Solve:
1. Total
Income of Two-Person Households. In
1993, there were about 31.2 million two-person households in the
2.
3. Stars. It is estimated that there are 10 billion trillion stars in the known universe. Express the number of stars in scientific notation.
4. Closest Star. Excluding the sun, the closest star to Earth is Proxima Centauri, which is 4.3 light-years away (one light-year = 5.88 X 1012 mi). How far, in miles, is Proxima Centauri from Earth? Express the answer in scientific notation.
5. Earth vs. Sun. The mass of the Earth is about 6 X 1021 metric tons. The mass of the sun is about 1.998 X 1027 metric tons. About how many times the mass of Earth is the mass of the sun? Express the answer in scientific notation.
6.
7. Proctor & Gamble. In a recent year, Proctor & Gamble led the nation’s advertisers by spending $2.777 billion on advertising (Source: Advertising Age) (1billion = 109).
Convert to Scientific Notation:
1. 28,000,000,000
2. 4,900,000,000,000
3. 907,000,000,000,000,000
4. 168,000,000,000,000
5. 0.00000304
Convert to Decimal Notation:
1. 8.74 X 107
2. 1.85 X 108
3. 5.704 X 10-8
4. 8.043 X 10-4
5. 10-8
Multiply:
1. (3 X 104)(2 X 105)
2. (3.9 X 108)(8.4 X 10-3)
3. (9.9 X 10-6)(8.23 X 10-8)
4. (1.123 X 104) X 10-9
Solve Using the Addition and Multiplication Principles:
1.
2.
13x-7 < -46
3.
8y-6 < -54
4.
30 > 3-9x
5.
48 > 13-7y
6.
7.
18-6y-4y <
63+5y
8.
2.1x+45.2 >
3.2-8.4x
9.
10. 
11. 
12. 8(2t+1) > 4(7t+7)
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Solve:
1. Banking. Find the amount in an account if $1000 is invested at 5%, compounded annually, for 2 years.
2. Time Loss. A watch loses 2 min in 10 hr. At this rate, how much will it lose 24hr?
3. Map Scaling. On a map, 3 in represent 225 mi. If two cities are 7 in apart on the map, how far apart are they in reality?
4. Weight of Muscles. The weight of muscles in a human body is 40% of total body weight. A person weighs 125 lb. What do the muscles weigh?
5. Population. The population of Rippington increased from 1500 to 3600. Find the percent of increase in population.
Solve:
1. Find the sum of the angle measures of a pentagon.
2. Find the measure of a complement of an angle of 79 degrees.
3. Find decimal notation for 89%.
4. Find percent notation for 0.674.
5. Find fractional notation for 65%.
Factor Completely:
1. x2+5x+6
2. y2-11y+28
3. 4+4x+x2
4. x+x2-4x
5. 49+56y+16y2
6. p2-9
7. –64+m2
8. a2-b2
9. 49x2-216
10. 27x3-13x
11. 18x3+12x2+2x
12. 162x2-82
13. x8-28
14. 9x18+48x9+64
15. 48x2-3
16. 20x3-4x2-72x
17. 3b2-17ab-6a2
18. 2mn-360n2+m2
19. p2q2+7pq+6
20. 16-p4q4
21. 15a4-15b4
22. 81a4-b4
23. c3-64
24. y3+125
25. x3+1
26. 8a3+1
27. 27x3+1
28. y3-8
29. 
30. 
Multiply and Simplify:
1. 
2. 
3. 
4. 
5. 
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Divide and Simplify:
1. 
2. 
3. 
4. 
5. 
Add and Simplify:
1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
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Solve:
1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 
19. 
20. 
21. 
22. 
23. 
24. 
25. 
26. Find the
x-intercepts: 
27. If 
, find f(0), f(1), and f(2)
28. Solve for
t: 
29. Solve for
b: 
Simplify:
1. 
2. 
3. 
4. 
5. 
6. 
7. 
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Solve by substitution method:
1. 
2. 
3. 
Solve by elimination method:
1. 
2. 
3. 
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Simplify by factoring:
1. 
2. 
3. 
4. 
5. 
Add or Subtract.
Simplify by collecting like radical terms.
1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
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Solve:
1. The length of a rectangle is three times the width. The area is 48 cm2. Find the length and the width.
2. The current in a stream moves at a speed of 2 km/h. A boat travels 24km upstream and 24 km downstream in a total time of 5 hr. What is the speed of the boat in still water?
3. Zack mows the backyard in 40 min, while Angela can mow the same yard in 50 min. How long would it take them, working together with two mowers, to mow the yard?
4. By checking work records, a plumber finds that Rory can fit a kitchen in 12 hr. Mira can do the same job in 9 hr. How long would it take if they worked together?
5. Morgan
can proofread 25 pages in 40 min.
6. A chef is planning meals in a refreshment tent at a golf tournament. The number of servings S of meat that can be obtained from a turkey varies directly as its weight W. From a turkey weighing 14 kg, one can get 40 servings of meat. How many servings can be obtained from an 8-kg turkey?
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